What is the formula to calculate population growth/rate?

Question

How do I use the formula for this word problem:

A small country that had 20 million people in 1990 has experienced exponential growth in population of 4% per year since then. Write an equation that models this situation and use your equation to determine when the population will double.

I know my formula ends up being:

P(n) = 20 x (1.04)^n

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Answer 1 · 2016-08-25T13:10:02

P(n)=P(0)e^(kt)

If P(n)=2*P(0) (n years later population will be double of the initial one).

Then #2=e^(k*t)#

t= years
k=population growth rate per year (which is 0.04)
Note that there is no limiting factor (or carrying capacity) in this situation.

Compute #2=e^(k*t)#

#ln 2=t*0.04#

#0.69314718/0.04 = t#

#t=17.33 years#

Again I underline there is no upper limiting factor. Population growth is exponential.